相容双有限domain及相关范畴性质  

Consistently Bifinite Domain and Some Properties of Relevant Category

作　　者：张滦云[1] 王戈平[2] 

机构地区：[1]淮海工学院数理科学系,江苏连云港222005 [2]徐州师范大学数学系,江苏徐州221009

出　　处：《南京师大学报（自然科学版）》2005年第1期36-41,共6页Journal of Nanjing Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10371079)

摘　　要：　将建立在dcpo上的双有限domain等概念推广到相容定向完备偏序集上,定义了相容定向完备偏序集上的逼近单位、有限分离、相容双有限domain等概念,给出了相容双有限domain的等价命题.并从范畴学的角度考察证明了以相容双有限domain为对象,Scott连续映射为态射的范畴CBF是笛卡儿闭范畴.还讨论了相容定向完备偏序集及相容代数domain上的几个性质.This paper generalizes some concepts such as bifinite domains from dcpos to consistently directed complete posets, defines concepts of approximate identity, finitely separated, consistently bifinite domains on consistently directed complete posets, and provides an equivalent proposition of consistently bifinite domains. Then it inspects and proves that the category CBF of consistently bifinite domains with Scott-continuous function is Cartesian closed in terms of category theory. In the end, It also discusses some properties on consistently directed complete posets and consistently algebraic posets

关 键 词：相容代数domain 相容双有限domain 笛卡儿闭范畴 

分 类 号：O153.1[理学—数学] O189.1[理学—基础数学]